Abstract
We show that for Gibbs measures on self-conformal sets in () satisfying certain minimal assumptions, without requiring any separation condition, the Hausdorff dimension of orthogonal projections to k-dimensional subspaces is the same and is equal to the maximum possible value in all directions. As a corollary we show that Falconer’s distance set conjecture holds for this class of self-conformal sets satisfying the open set condition.
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